It's the holiday season again. Christmas is here, and Hanukkah is recently past. For many people today these holidays have a significance
that is purely cultural. However, many others still observe these holidays as religious occasions.

I'd like to take this opportunity to spread some "Joy to the World" by stating an important point about religion - not any particular religion,
but religion in general. Here it is:

Science has not debunked religion and never will succeed in debunking religion.

The reason is simple: the most important claims of religion cannot be tested by scientific means. Science can't prove these beliefs right or wrong,
or even prove them highly improbable. Today's noisy militant atheists might not like this fact, but it is a fact nonetheless.

Science can pass judgment on religious beliefs that are scientifically testable. For example, science has ruled out creationism - the belief
that living species and the Earth are results of miraculous acts of creation instead of products of natural processes like evolution. Clearly science
can debunk some religious beliefs. Many traditional religious beliefs have gone out the window for this reason. We can expect some
more to go out the window in the future. However, science cannot debunk the really important ideas in religious thought.

Here's an example.

For many religions, the most important religious doctrine is the belief that there is a God. Who, or what, is God supposed to be? There are
different opinions. Some people think of God as a ghostly being, perhaps cruel and violent, who created natural objects through supernatural acts.
Some believers picture God this way; so do some atheists. But is such a "God" really worthy of the name "God"? Is he (or she, or it) worthy of
our unswerving love? And why should we believe in those miraculous acts of creation when science offers better explanations of natural phenomena?
People of conscience and reason often have trouble with this idea of God - and well they might!

If we think about the religious feelings of the more conscientious and thoughtful believers, we find that the God they believe in is not an angry ghost.
Instead, their God might be described as a supremely good being - a being embodying great love, kindness, and spiritual
beauty. If there is such a being, then He, She or It is indeed
worthy of our love. (Believers who think of God this way often also believe that God is a supernatural creator. However, this other belief is not really
indispensable to their thinking. They could believe in a good God even if God didn't create the universe. What matters in their daily lives is not how
the universe started, but that God is good.)

Science can't debunk the idea that there is a supremely good being. The reason is simple. This idea of God depends on the idea of the
good - and science, acting alone, cannot make judgments about what is good!

It is impossible to prove or disprove moral judgments, like "mercy is good" or "hate is bad," by means of scientific methods alone. The same
goes for aesthetic judgments, like "This meadow is beautiful." It isn't possible to confirm or disconfirm such statements through scientific methods
alone, without resorting to other ways of knowing, such as moral and aesthetic reasoning. This isn't news to philosophers, but nowadays it's too
easily forgotten. The possibility that values are partly a matter of opinion doesn't change all this. Even if someone claimed (implausibly)
that nothing has objective value, that claim still wouldn't be scientifically testable. Needless to say, scientists can make value judgments
on their own, as human beings. However, no one can succeed in making value judgments using scientific methods alone. Science can study some
questions about morality, like what makes people behave in ways commonly regarded as moral. However, science cannot say whether any
moral standard (regardless of its origin) is objectively right.

Now back to the subject of God. We have seen that the idea of a supremely good being is one idea of God - and such a God is much more
admirable than the angry ghost. So here's the big question: How can science prove that there's no supremely good being, when science,
acting alone, can't even tell us whether anything is good or evil? The answer is simple: it can't. The very idea of science proving that there is no
supremely good being is silly. It's like trying to prove scientifically that pulling the cat's tail is naughty. Any "scientific" argument that pretends to
prove such conclusions must involve hidden side assumptions that are not scientific. Any plausible argument for or against God will be philosophical
rather than purely scientific.

Some atheists have tried to debunk God on scientific
grounds by arguing that God would have to be a very complex being, and that very complex beings are intrinsically improbable.
This argument starts from an inadequate concept of God, but
the argument also has another, more glaring flaw. The argument overlooks the fact
that the improbability of complex beings is a consequence of the laws of nature. If the laws of nature had been different, things might have had probabilities vastly
different from the ones they actually have. If we take God to be supernatural (as many people do), then we don't know whether the laws of nature apply
to God - so we have no way to tell whether God would be improbable or not. If, on the other hand, God is natural (as some people believe), then the
complexity of God is just all or part of nature's complexity. Either way, the argument that God is too complex to be believable is bad logic on a
monumental scale. This objection to the argument certainly doesn't prove there is a God, but it shows that one "scientific" line of argument against God is wrong.
For the details of this objection, and for some other objections to the same argument, see this paper. Similar
problems face any argument that compares God to "Russell's teapot" or other
improbable natural objects.

Until now I've been using the idea of God as an example of a scientifically untestable religious belief. Certain other important religious beliefs are like this too.

For example, there is the idea of an afterlife. Scientists often seem to think that science has debunked the afterlife once and for all. They argue that science has proven the self or
personality to be a feature of the brain. Therefore (the argument goes) the self must disappear when the brain dies. But does this argument really work? Even if your self is only
an attribute of your brain, why can't another brain have the same attribute after the end of your present brain?

It's nothing special for an attribute of a physical object to occur later in another physical object. Here's an example: Suppose that there were only one object having a certain
shade of green. Then that object is destroyed. Later, a painter mixes new paint and just happens to create an object having exactly that same shade of green. In this example,
one object has an attribute (a particular color) for a while - and later, after a delay, another object has the same attribute. Yet nothing passed between the two objects, and nothing miraculous happened.

If your self or identity is an attribute of your brain, couldn't that attribute occur again later in another object (brain)? The answer isn't
obvious; when you begin to think carefully about the question, the
question turns out to be quite complicated. The important thing is that when we look at the afterlife this way, we find that the scientific view of the mind cannot rule it out.
Even if the self is an attribute of the brain, it's still logically and physically possible that there is an afterlife. What is more, the existence of an afterlife doesn't have to involve any kind of
complexity that would make it statistically improbable. (See here for more details.)
This certainly doesn't prove there is an afterlife - but it shows that the scientific view of the mind doesn't rule out an afterlife of some kind. The existence of the afterlife is a
philosophical question, not a scientific one.

This post is not meant to persuade anyone to believe in God or in an afterlife. (Fanatical atheists, take note of this last sentence before you start calling me a hack, a fairy believer,
and all your other usual hate words.) Also, I'm not asking anyone to believe in standard forms of religion. (As you know if you perused my website, my own ideas about religion
aren't exactly standard and tend toward the disgustingly logical.) I'm just trying to point out that science cannot debunk the essential ideas of religion. Science can dispose of some
outdated forms of belief, but science has little to do with the most important ideas at the heart of religion. So-called "scientific" disproofs of religion are simply pseudoscience.
Away with them, along with the flat earth theory!

Now go have a very happy holiday season. Of course, this might be difficult if you are a militant atheist. In that case, you might prefer to spend the time putting the
evil eye on me - an act just as rational as any so-called "scientific" argument against God.

In my past writings I have had a lot to say about the reality of abstract objects. I have argued that these entities are real, though not in the same way that concrete things (like tables and chairs) are real. This is one of the standard philosophical positions about abstract objects [1]. One of the main lines of argument against this position is that accepting abstract objects adds unnecessary new things to the world. (In other words, accepting abstract objects supposedly violates Occam's Razor.) I do not believe that abstract objects pose any threat of this sort. The claim that abstract objects exist tells us little beyond what we already know when we say that objects have properties or relationships. See my earlier writings (here, here and here) for more about these ideas.

In this post I'd like to explore another, far more daring question about abstract objects: Might everything be abstract?

The speculation that everything might be abstract has precedents in philosophy. One precursor is the idea that the world is basically mathematical. This goes back to Greek philosophy (especially the Pythagoreans). The idea that the world might actually be a mathematical object occurs in modern times [2]. At first glance, the possibility that everything might be abstract seems implausible. How could everything be abstract when there's this solid, obviously concrete world around us? How could physical objects be abstract when abstract objects seem to be placeless, timeless, and devoid of the ability to cause events? (These are negative features that philosophers often attribute to abstract objects [3].) Also, how could everything be abstract when abstract objects are mainly just features of concrete objects? Wouldn't there have to be some concrete objects to begin with?

These worries become less pressing if we can begin to overcome the habit of picturing all abstract objects as intangible, ethereal, or not quite real. The worries might lose force even more when we explore the relationship between ordinary physical objects and their properties.

Before starting this exploration I'll make a few preliminary remarks about abstract objects.

If we accept the reality of abstract objects, then our picture of reality has room for many different kinds of existence. Tables and chairs are real, but so are properties like shapes and colors. Stars and galaxies are real, but so are relationships like being more massive than and being hotter than. Atoms and molecules are real, but so are mathematical items, like the set of all atoms in a DNA molecule (not the same as the molecule itself!) and the number of atoms or nuclei in a hydrogen molecule.

Mathematical logicians often think of abstract objects as forming systems of "logical types," or domains of abstract objects of different levels. For example, we might take physical objects to have logical type 0. Then a property of physical objects (like rectangularity) is of logical type 1. A property of a property of physical objects (like the property of being a shape property) is of logical type 2. And so on through type 3, 4,.... There also can be other types not in this series, such as types of relations. Logicians sometimes visualize an endless tower of logical types starting with the world of concrete things. Set theorists use a more flexible idea of levels, but the core idea is the same.

Often it's convenient to think in terms of towers of types, but we shouldn't get stuck thinking that every abstract object has to belong to one of these types. We need to keep an open mind and consider other possibilities - like sets that are members of themselves, or properties that are properties of themselves, or perhaps even two sets that are members of each other. Some logicians and mathematicians study things like these, mostly under the banner of "non-well-founded sets."

With these preliminaries in mind, I'd like to ask a key question: Where is the dividing line between concrete things and abstract objects?

I tried to answer this question in a talk called "Abstract Objects and Physical Reality," which you can find in a book of mine called The Unfinishable Book. (As of the date of this post, the book is downloadable for free - where "free" means "free except for the usual internet charges.") The gist of my answer is that there is no uniquely determined boundary between concrete objects and abstract objects.

This idea is not really new. Both Carnap's Aufbau [4] and Quine's thesis of ontological relativity [5] recognized that the choice of a domain of "concrete" entities might not be unique. However, what I'm proposing here is different from these earlier ideas. I am not embracing Quinian ontological relativity, and I am not proposing to use logical constructs, Aufbau-style, as substitutes or ersatzes for anything. I am only proposing that there is no unique domain of objects which alone are objectively "concrete."

Here is a brief introduction to the argument.

First, a bit more background on abstract objects. Concrete physical objects seem to be very different from abstract objects. However, when we begin to analyze physical objects, we find out that a physical object is an item that unites, or joins together, several properties and relations. A physical object has properties and relations which determine what the object is like. A physical object without properties and relations would be essentially "nothing." The most useful thing we could say about such an indefinite object is that it is able to hold several properties and relations together.

If we mentally distinguish a concrete object from its properties and relations, what is left of the object? Almost nothing! There would be only the factor that unites the properties and relationships.

Some philosophers have held that this uniting factor is a "bare particular" - a sort of simplified concrete object that does little more than hold together its properties and relations. Other philosophers (the "bundle theorists") deny bare particulars and view the uniting factor as something abstract, like a class.

Now here is the key insight behind my answer: It's hard to believe that a "bare particular" really is a concrete object. A bare particular looks more like a special property, shared in common by the properties and relations that it unites. I would argue that there is no significant contrast between a bare particular and a special property of this kind. Thus, if there is a bare particular, a concrete object is, at bottom, an abstract object. If there is no bare particular (and bundle theory is right), then a concrete object is, at bottom, abstract too. Either way, a concrete physical object can be analyzed into a combination of abstract objects of some kind.

If this view of existence is true, then there is no strong dividing line between the concrete and the abstract. The difference depends on where you begin your analysis. If you take concrete physical objects as the starting point, and don't try to analyze them into entities of other kinds, then you get the usual picture of abstract objects. You find that there are concrete objects, and then there are the various properties, relations, properties of properties, etc. of those objects. However, if you start your analysis with entities usually called abstract, you can portray concrete objects as properties or classes of them.

An obvious (but weak) objection to this view is that it can lead to circles of attribution, in which a physical object is a feature or class of abstract objects, while abstract objects are in turn features of physical objects. I don't think we should worry about these circles. They aren't vicious. They are no more illogical than the non-well-founded sets that I mentioned earlier. We can always postpone the circle in practice, by taking some fixed domain of objects as "concrete" and building up from there. The fact that everything is analyzable into other items doesn't make anything less real.

Another obvious objection is that physical objects have features that abstract objects don't have. For example, physical objects have spatial and temporal locations and causal powers - features that philosophers often deny to abstract objects. I don't think this objection is fatal either. Bare particular and bundle theories have to face this objection too. (Where is a bare particular located, when its spatial location has been stripped away along with its other properties? The "bundle" in bundle theory is an abstract object such as a class; how can it "be" a locatable, causality-ridden physical thing?) If this objection is not fatal to those theories, then it is not fatal to what I am proposing here.

For further details of the above argument, read Talk #9, called "Abstract Objects and Physical Reality" in The Unfinishable Book.

What, then, is the answer to our initial question, "Might everything be abstract?" The answer is "yes - in a way." Any given thing might be analyzable in a way that shows it to be an abstract object. However, that wouldn't prevent us from labeling some objects as concrete and using them as a "ground floor" for defining further abstractions. Normally we use physical objects as the concrete objects, but do we have to? Physical objects are the objects that seem most concrete to us - but perhaps that's just because we can detect many of them through our sense organs, which also can be analyzed as abstract objects if we have the nerve! (Pun intended.)

*****

Concluding Cryptic Remark:

And now, for something really strange to think about.

Normally we equate the "world" to the world of concrete physical objects. We tend to regard other entities as mere features of that world. To borrow a term from mathematics, this amounts to taking a kind of "section" through the universe - picking out a preferred set of objects and treating them as basic. Usually the entities we treat as basic are the concrete physical entities. We regard them as the basic "world," with all other things mere features of that world.

What if we broke away from this unnecessary practice? What if we took a different "section" by choosing some different family of abstract objects as basic? What if we regarded all other entities, including our familiar physical objects, as mere features of those other objects? What would the resulting view of reality be like? Can we even do this without inconsistency?

This proposal sounds a bit like certain relativism-soaked ideas in philosophy - I'm thinking especially of Quine's ontological relativity thesis. However, it's not the same, because my proposal begins with a domain of real entities. All the abstract objects really exist, each in its own way. What is "relative" is the classification into abstract and concrete.

A conjecture: I suspect that if we began with data structures in the human brain as basic objects, we might arrive at a picture of reality in which the "basic" entities are experiences or their contents, and the physical world is a system of features of experiences or of their contents [6]. This would be a form of metaphysical idealism. However, this idealism would be fully compatible with naturalism, because both these viewpoints are just alternative analyses of the same world. See Chapter 13 in my book From Brain to Cosmos for my early thoughts on the possibility of a naturalistic idealism.

End of Cryptic Remark.

--------------------------

Notes

[1] The position that abstract objects are real is called ontological realism or platonism. My version of it is a modest version.

[2] Rudy Rucker wrote about the idea that everything is a set. See pp. 200-201 in Rucker's book Infinity and the Mind: the Science and Philosophy of the Infinite (Boston, Basel and Stuttgart: Birkhäuser, 1982).

[4] Carnap's Aufbau exists in several editions, including the following: Carnap, Rudolf (1928). The Logical Structure of the World. In The Logical Structure of the World; Pseudoproblems in Philosophy, trans. R. A. George (Berkeley: Univ. of California Press, 1969).

[6] This seems reminiscent of what Carnap tried in the Aufbau, but actually it's different from the ground up (pun intended again). We aren't substituting logical constructions for anything. There is just a domain of objects, and there are different ways of classifying them.

Sometimes people ask me whether I am an atheist, a theist, or an agnostic. Instead of giving simplistic answers to these questions, I'm going to take a few minutes to explain what I really think.

1. Am I a theist?

Theism is the belief that there is a supernatural God who created the universe and intervenes in it. Some people use the word "theism" to mean belief in a deity of any kind at all. However, this isn't the way the word usually gets used today. Usually "theism" is used to mean belief in a supernatural God who created and intervenes in the universe. Here I'll use "theism" in that sense.

According to this "standard" definition, I am not a theist. My problem with theism is not with the idea of a supreme being of some kind; my main problem is with the idea of the supernatural. I'll say more about that later.

Now that I've said this, I can almost hear the atheists printing my membership card. But wait! Things aren't as simple as they seem...

2. Am I an atheist?

I have a one-word answer to this question. However, the answer would be very misleading if I didn't explain a few things first.

The word "atheist" gets flung around rather freely today. However, labeling someone an "atheist" can be philosophically tricky. The problem with the word "atheist" is that the meaning of the word depends on which idea of God you accept. For example, a Christian might call an unbeliever in the biblical God an "atheist" just because that person accepts a concept of a supreme being different from the biblical God. Modern atheists sometimes make a similar mistake. They define the word "God" to mean a supernatural creator. Then, when they argue against belief in a supernatural creator, they think they are debunking God. The truth is more complex: you can believe in God without believing in a supernatural creator.

Philosophy and religion, both Eastern and Western, contain several different ideas of a supreme spiritual reality or supreme being. Some of these ideas do not portray the supreme being as a supernatural creator. I don't mean just the well-known "scientific" pantheism that equates God to the physical universe. There also are other ideas of God that don't involve supernatural creation but that don't equate God to the physical universe. Some of these ideas can do without belief in the supernatural. (Click here and here for further details.) Those who define the word "God" to mean only a supernatural creator, and who refuse to admit that there are other views of God, are just redefining the word "God." The idea that God is a supernatural creator is only one way to think about God. There are other ways.

Although I don't accept theism (defined as above), I am not anti-spiritual. I think the universe has a spiritual aspect to it. This spiritual aspect is not supernatural; humans can learn about it through the rational methods of philosophy (no religious faith required). I even think there is a supreme spiritual reality of sorts. This is not supernatural, but it fits pretty well with the philosophers' definition of a "greatest possible being" - a definition that I consider crucial to the idea of God. For more details, read this document.

So, do I believe in God? Those who insist on defining God as supernatural will conclude that I don't believe in God. However, I have a different answer: I do believe in God. Not the supernatural God of theism, but a supreme spiritual reality that's worthy of the name "God." My one-word answer to the question "Am I an atheist?" is "No."

If you think "God" can only mean a supernatural creator, then you might prefer to call me an atheist. My feelings won't be hurt, but I'll tell you that your definition of God needs some repairs!

3. Am I an agnostic?

My answer to the atheism question shows that I am not agnostic about the existence of a supreme spiritual reality. I think reason supports that idea. However, I am an agnostic of sorts about the existence of the supernatural. I don't believe there is anything supernatural (though there might, of course, be things in nature that seem supernatural to us). However, I don't know of any convincing argument for the nonexistence (or even the extreme improbability) of the supernatural. Thus, I am neither a believer nor a hard-core disbeliever in the supernatural. Followers of supernatural religions might want to consider me an agnostic for this reason. But I am not agnostic about the existence of some kind of supreme spiritual reality.